The Fayet-Iliopoulos term and nonlinear self-duality

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The N = 1 supersymmetric Born-Infeld action is known to describe the vector Goldstone multiplet for partially broken N = 2 rigid supersymmetry, and this model is believed to be unique. However, it can be deformed by adding the Fayet-Iliopoulos term without losing the second nonlinearly realized supersymmetry. Although the first supersymmetry then becomes spontaneously broken, the deformed action still describes partial N = 2 to N = 1 supersymmetry breaking. The unbroken supercharges in this theory correspond to a different choice of N = 1 subspace in the N = 2 superspace, as compared with the undeformed case. Implications of the Fayet-Iliopoulos term for general models for self-dual nonlinear supersymmetric electrodynamics are discussed. The known ubiquitous appearance of the Volkov-Akulov action in such models is explained. We also present a two-parameter duality-covariant deformation of the N = 1 supersymmetric Born-Infeld action as a model for partial breaking of N = 2 supersymmetry.